Question

Given that n(A) = 12, n(B) = 7
and n(AUB) = 10
Find n(ANB)
Pls show working

Answer 1

Given:

`n(A)=12`

`n(B)=7`

`n(A\cup B)=10`

To find:

The value of
`n(A\cap B)`.

Solution:

We know that,

`n(A\cup B)=n(A)+n(B)-n(A\cap B)`

After substituting the given values, we get

`10=12+7-n(A\cap B)`

`10+n(A\cap B)=19`

`n(A\cap B)=19-10`

`n(A\cap B)=9`

Therefore, the value of
`n(A\cap B)` is 9.

Note: The values are not correct because
`n(A)` cannot be greater than
`A\cup B`. The steps of solving these types of question are shown above.